Let's denote the unknown number as [tex]\( x \)[/tex].
According to the given problem, we can set up the following equation:
[tex]\[ 2x + (x - 5) = -41 - x \][/tex]
This equation states that if you take twice the unknown number ([tex]\( 2x \)[/tex]) and add it to 5 less than the number ([tex]\( x - 5 \)[/tex]), you will get the same value as subtracting the number ([tex]\( x \)[/tex]) from -41.
Now let's solve the equation step by step:
1. Combine like terms on the left side of the equation.
[tex]\[ 2x + x - 5 = -41 - x \][/tex]
This gives us:
[tex]\[ 3x - 5 = -41 - x \][/tex]
2. Add [tex]\( x \)[/tex] to both sides of the equation to move the [tex]\( -x \)[/tex] on the right side to the left side.
[tex]\[ 3x - 5 + x = -41 - x + x \][/tex]
This simplifies to:
[tex]\[ 4x - 5 = -41 \][/tex]
3. Add 5 to both sides of the equation so that we can isolate the term with [tex]\( x \)[/tex] on the left side.
[tex]\[ 4x - 5 + 5 = -41 + 5 \][/tex]
This simplifies to:
[tex]\[ 4x = -36 \][/tex]
4. Divide both sides of the equation by 4 to solve for [tex]\( x \)[/tex].
[tex]\[ \frac{4x}{4} = \frac{-36}{4} \][/tex]
This gives us:
[tex]\[ x = -9 \][/tex]
Thus, the number we are looking for is [tex]\( -9 \)[/tex], which corresponds to option A.
